Question

triangle lmn is similar to triangle opq. find the measure of side qo. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Use the property of similar triangles

For similar triangles \( \triangle LMN\) and \( \triangle OPQ\), the ratios of corresponding sides are equal. That is \(\frac{MN}{PQ}=\frac{LN}{OQ}\).
Given \(MN = 5\), \(LN=14\), \(PQ = 21\). Let \(OQ=x\). Then the proportion is \(\frac{5}{21}=\frac{14}{x}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(5x=14\times21\).
First, calculate \(14\times21 = 294\). So, \(5x = 294\).
Then, solve for \(x\) by dividing both sides by \(5\): \(x=\frac{294}{5}=58.8\).

Answer:

\(58.8\)